There is an ongoing need for improved computerized tools which facilitate the locating of new oil and natural gas reservoirs, the optimizing of production from new and existing reservoirs, and for other related geological applications. Some embodiments of the present invention relate to stratigraphic grids (SGrids) that provide a stair-stepped approximation of a geological discontinuity. One technique for producing such an SGrid is disclosed in US 2008/0243454, of one of the present inventors.
As was discussed in the background section of US 2008/0243454, incorporated herein by reference in its entirety, many conventional tools for generating a stratigraphic grid suffer a number of drawbacks. For example, these tools may incorrectly model “dying faults,” they may produce an inaccurate geological model in the presence of faults intersecting each other in an “Y” or “X” manner, or they may produce degenerated and/or distorted cells. When simulating flow via through a geological terrain represented by one of these conventional stratigraphic grids, these degenerated and/or distorted cells may yield less-than-optimal results.
US 2008/0243454 describes an improved ‘dual cookie cutter’ partitioning technique for building a stratigraphic grid (SGrid). In some embodiments, the ‘dual cookie cutter’ technique disclosed in US 2008/0243454 may produces a grid model that approximate fault surfaces in a stair stepped way, regardless of the complexity of the horizons and/or faults. In one non-limiting example, the cells generated by the dual cookie cutter partitioning technique are hexahedral cells having angles that approximate right angles—nevertheless, as was noted in US 2008/0243454, this is not a limitation.
FIG. 1 illustrates (i) a fault network of faults 1001, 1002 and 1003 and (ii) an SGrid 1004 which models the Earth's subsurface in the presence of the faults. The SGrid provides a stair-step approximation of these faults both in the horizontal and vertical direction.
FIG. 2A more clearly illustrates the “stair-step” approximation of faults 1001-1004. SGrid of FIG. 2A includes four sub-regions which are determined according to faults 1001-1004: (i) a first sub-region (labelled “Sub-region I” 110 or the black region) (ii) a second sub-region (labelled “Sub-region II” 120 or the dark grey region); (iii) a third sub-region (labelled “Sub-region III” 130 of the light grey region) and (iv) a fourth sub-region (labelled “Sub-region IV” 140 or the white region).
As is evident by comparing FIG. 1 to FIG. 2A, the boundary between the first 110 and second subregions 120 in FIG. 2A approximates fault 1001 in certain locations. Because the cells of FIG. 2A are substantially hexahedral cells, the intersection of fault 1001 with the ‘top’ reference horizon (see paragraph [0004] of US 2008/243454 for a definition of reference horizons) is approximated by a series of straight lines that are either parallel to each other or at right angles to each other—hence the ‘stair-step’ approximation of the geological discontinuity.
FIG. 2B is an exploded view of the SGrid of FIG. 2A.
The broken white line of FIG. 2C illustrates the “stair-step” approximation of fault 1001 provided by the ‘border’ surface between sub-region I 110 and sub-region II 120 (i.e on the ‘side’ of the border of sub-region I 110). The facets enclosed by the broken white line collectively approximate a fault (or a line formed by the intersection of multiple faults). One salient feature of these facets is that they are substantially rectangular shaped, though as discussed below (and within US 2008/243454), this should not be construed as a limitation for the dual-cookie cutter method.
The broken line of FIG. 3A illustrates a horizontal stair-step border between cells of the dark grey region and cells of the light grey region. FIG. 3B illustrates the relationship between the ‘stair-stepped’ border and a curve that is an intersection between fault 1002 and the reference horizon. As is illustrated in FIG. 3C, cells (marked with an “X”) of sub-region III 130 may be internally divided by the fault. This is one feature that is provided by ‘dual-cookie cutter’ technique (see FIG. 13 of US 2008/0243454 and compare to FIG. 12 of US 2008/0243454) according to some embodiments.
In FIG. 3D, the cells of region II 120 that border the ‘internally-divided’ cells of sub-region III 130 are marked with the letter Y. The actual fault 1002 is illustrated in FIGS. 3C-3D, and it is clear from the figure that the ‘stair-step’ outline (i.e. shown in the bold broken line—this outline delineated the ‘border’ between cells of sub-region II 120 and cells of sub-region III 130) approximates fault 1002 B (or as illustrated in FIGS. 3C-3D, the intersection between fault 1002 and reference horizon).
In FIGS. 3E-3F, certain cells that are proximate to multiple geological discontinuities (i.e. both faults 1002 and 1003) are illustrated including cells marked with a “Z”, a “T” a “V” and a “U.”
It is noted that the dual-cookie cutter technique may yield ‘horizontal stair-steps’ as illustrated in FIG. 3, as well as “vertical stair-steps’ illustrated in FIG. 4 where the ‘substantially vertical surface’ of FIG. 4B is typically a surface that is substantially perpendicular to a ‘reference horizon’
In FIG. 4B, some of the cells that are internally divided by a fault are marked with a “+.”
FIG. 4C shows a part of the SGrid represented in the earlier figures where the cells internally intersected by the fault 1001 are represented in dark grey.
In some implementations of the dual cookie cutter algorithm, it is possible to generate two ‘competing intermediate grids’ which may contradict each other in one or more cells. Each ‘intermediate grid’ may represent a specific sub-region and have ‘stair-step properties.’ However, in ‘intersection regions’ near the geological discontinuity where the intermediate grids ‘contradict each other,’ it is possible to ‘resolve’ the contradicting
By ‘contradict each other,’ we mean that there is at least one location in 3D space where according to the first ‘intermediate grid’ which models sub-region ‘i’ (i is a positive integer) the location in space ‘belongs to’ sub-region i, while according to the ‘second intermediate grid the location in space ‘belongs’ not to sub-region j. When these two intermediate grids are superimposed upon each other, overlapping cells may be generated.
FIG. 5A is a flow chart of a routine for generating a non-contradicting SGrid with a stair-step representation of a geological discontinuity. In step S311, a first stair-stepped intermediate grid SGrid_INT—1 is generated—see, for example, the grid of FIG. 5B. In step S315, a second stair-stepped intermediate grid SGrid_INT—2 is generated—see, for example, the grid of FIG. 5C. FIG. 5D-5E illustrate a single SGrid that is SGRID_INT—1 superimposed upon SGRID_INT—2—it is possible to see overlapping cells at the location of the geological discontinuity.
In step S319, the two intermediate grid (which have overlapping cells) are resolved to provide a single stair-stepped approximation of the geological discontinuity (see FIG. 5F). In some examples, FIG. 5F is the ‘final product’ of the dual cookie cutter. The SGrid of FIG. 5F is sub-portion of the grids of FIGS. 1-3.
In some examples, this of step S319 resolving may require merging cells and/or eliminating vertices and/or eliminating cells in order for the ‘contradictory location’ to only be a part of a single sub-region.
One common feature of both the intermediate grids of FIGS. 5B-5D and of the ‘resolved grid’ of FIG. 5F is that both grids may include cells that are internally divided by a geological discontinuity (e.g. a fault).
FIGS. 6A-6B relate to the example of FIG. 3 where individual cells in sub-region II 120 are labelled as 240, while individual cells in sub-region III 130 are labelled as 260.
Embodiments of the present invention relate to methods and apparatus for transforming SGrids that include “vertical” stair-step representations of geological discontinuities in a direction perpendicular to the reference horizons.
Although the SGrid 1004 of FIG. 1-5 was generated using the dual-cookie cutter stratigraphic grid partitioning technique of US 2008/0243454, it is appreciated that other techniques may be utilize to generate ‘stair-step’ approximations of geological discontinuities.
As noted above, although many examples of dual cookie cutter partitioning technique relate hexahedral cells having angles that approximate right angles and faces nevertheless, as was noted in US 2008/0243454, this is not a limitation. Thus, the dual cookie cutter technique may be employed to generate cells whose top and bottom facets (i.e. which are each substantially coplanar with a local plane tangent to an horizon) have a polygonal shape rather than quadrangular shape.
In one example, the top and bottom facets (i.e. which are each substantially coplanar with a local plane of a ‘reference horizon’) have a triangular shape, and the cells generated using the dual cookie cutter technique have the shape of a triangular prism. In another example, the top and bottom faces have a hexagon shape, and the cells. In both of these cases, the lateral cells are quadrilateral (for example, substantially rectangular) and approximately orthogonal to the local plane of a reference horizon. In both of these cases, it is possible that the approximation of the geological discontinuity (e.g. fault) within the local plane of a reference horizon may be ‘zig-zag’ rather than ‘stair-stepped,’ the approximation of the geological discontinuity in the direction normal to the local plane of a reference horizon (i.e. in substantially the ‘vertical’ direction) remains a ‘stair-stepped’ approximation. This is because even these cells have a quadrilateral (e.g. substantially rectangular) shape in the direction normal to the local plane of a reference horizon.
In the examples discussed above, the dual cookie cutter was used to generate a stair-stepped approximation of a fault that divides between two different sub-regions. This is not another limitation. In yet another example, cells may be divided according to intersection locations between a “dying fault” and a dual fiber of a column. In this case, the ‘dying fault’ may also be represented by a ‘stair-step’ representation—however, in this case, the stair-step representation of the dying fault would not be a ‘border’ between different sub-regions but rather would reside ‘internally’ within a single sub-region.